HW8 - 1 Physics 2210. Homework assignment 8. B 7.9.10...

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Unformatted text preview: 1 Physics 2210. Homework assignment 8. B 7.9.10 f(x)=|x| is an even function and has a period T= for this problem. The Fourier series should be f(x) = a 2 + a n cos( 2n x T ) n = 1 = a 2 + a n cos(2nx) n = 1 . a = 4 f(x)dx /2 = 4 xdx /2 = 2 , a n = 4 f(x)cos(2nx)dx /2 = 4 xcos(2nx)dx /2 = 1 n 2 [( 1) n 1] , for n=1,2, f(x) = 4 + 1 1 n 2 [(-1) n-1]cos(2nx) n = 1 = 4 2 1 (2n -1) 2 cos[2(2n -1)x] n = 1 . T&M 3.28 f(t) is an odd function and has a period T=2 / for this problem. The Fourier series should be f(t) = b n sin( 2n t T ) n = 1 = b n sin(n t) n = 1 . b n = 2 f(t)sin(n t)dt / = 2 sin(n t)dt / = 2 n [( 1) n 1] , for n=1,2, f(t) = 2 1 n [1- (-1) n ]sin(n t) n = 1 = 4 1 (2n -1) sin[(2n -1) t] n = 1 ....
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HW8 - 1 Physics 2210. Homework assignment 8. B 7.9.10...

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